*Published Paper*

**Inserted:** 2 dec 2002

**Last Updated:** 30 sep 2012

**Journal:** Calc. Var.

**Volume:** 18

**Number:** 4

**Pages:** 373-400

**Year:** 2003

**Notes:**

Preprint no.43, SFB 611, University of Bonn

**Abstract:**

We give new estimates for the Hausdorff dimension of the singular set of solutions to elliptic systems: $$ - \mbox { div } a(x,u,Du) = b(x,u,Du)\;.$$ \noindent If the vector fields $a$ and $b$ are HÃ¶lder continuous with respect to the variables $(x,u)$ with exponent $\alpha$, then, under suitable assumptions, the Hausdorff dimension of the singular set of any weak solution is at most $n-2\alpha$. We consider natural growth assumptions on $a(x,u,Du)$ with respect to $u$ and critical ones on the right hand side $b(x,u,Du)$ with respect to $Du$.